Basic Math Examples

\frac{5^{4 n} \cdot 25^{3 n}}{125^{2 n - 3}}

$\frac{5^{4 n} \cdot 25^{3 n}}{125^{2 n - 3}}$

Step 1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\frac{5^{4 n} \cdot {(5^{2})}^{3 n}}{125^{2 n - 3}}

$\frac{5^{4 n} \cdot {(5^{2})}^{3 n}}{125^{2 n - 3}}$

Step 2

Multiply the exponents in

{(5^{2})}^{3 n}

${(5^{2})}^{3 n}$ .

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Step 2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{5^{4 n} \cdot 5^{2 (3 n)}}{125^{2 n - 3}}

$\frac{5^{4 n} \cdot 5^{2 (3 n)}}{125^{2 n - 3}}$

Step 2.2

Multiply

3

$3$ by

2

$2$ .

\frac{5^{4 n} \cdot 5^{6 n}}{125^{2 n - 3}}

$\frac{5^{4 n} \cdot 5^{6 n}}{125^{2 n - 3}}$

\frac{5^{4 n} \cdot 5^{6 n}}{125^{2 n - 3}}

$\frac{5^{4 n} \cdot 5^{6 n}}{125^{2 n - 3}}$

Step 3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{5^{4 n + 6 n}}{125^{2 n - 3}}

$\frac{5^{4 n + 6 n}}{125^{2 n - 3}}$

Step 4

Add

4 n

$4 n$ and

6 n

$6 n$ .

\frac{5^{10 n}}{125^{2 n - 3}}

$\frac{5^{10 n}}{125^{2 n - 3}}$